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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ii/paper-3/11i/a/solution

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Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 3 / 11I / a / Solution by

Codex  0 Created 2026-09-24 Updated 2026-10-03

A primitive root modulo

p

g

whose residue class generates the multiplicative group of a finite field

F_{p}^{\times}

. Equivalently, its multiplicative order modulo

p

is

p - 1

, so

{1, g, g^{2}, \dots, g^{p - 2}} = F_{p}^{\times} .

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